State Republicans will “welcome” First Lady Hillary Rodham Clinton to New York Wednesday with an airport “beauty contest” for the best-looking Adirondack fly.

“We’re inviting members of the public to show up at the Binghamton airport in fly costumes so the First Lady, who obviously doesn’t know much about New York, can get an idea what a good Adirondack fly looks like,” state GOP Executive Director Brendan Quinn told The Post yesterday. “We’re going to offer the person who shows up with the best fly costume a free weekend at the Lake Placid Resort in the Adirondacks, where we know the winner will have a wonderful, fly-free, weekend.”

The Republican “contest” is aimed at reminding the First Lady – and New York voters – that one of her political aides contended two weeks ago that Mrs. Clinton and the president won’t vacation in the Adirondacks this summer because of an alleged fly problem.

The crack drew loud protests from Adirondack politicians, and reinforced the perception that Mrs. Clinton, who is eyeing a campaign for U.S. Senate – even though she has never lived in New York – has the potential to make political gaffes.

Meanwhile, two top New York Democrats who back Mrs. Clinton yesterday acknowledged that she might be using the Senate race as a stepping stone to the White House.

Rep. Charles Rangel (Manhattan), one of the first Democrats to urge her to run for the New York seat being vacated by Sen. Daniel Patrick Moynihan, said, “It doesn’t surprise me” that a would-be senator would “aspire” to be president.

“There’s something in the water those senators drink that allows all of them to believe that they should be the next president of the United States,” Rangel told NBC’s “Meet The Press.”

Rep. Nita Lowey (Westchester), who was eyeing the Senate seat until Mrs. Clinton expressed her interest in it, told “Fox News Sunday”: “I don’t know a senator that doesn’t have a twinkle in their eye and think about being the president of the United States.”

Meanwhile, former presidential aide George Stephanopoulos said the rampant grumbling that Mrs. Clinton is “just an opportunistic carpetbagger trying to use New York … as a stepping stone to higher office” is a “serious problem” for the First Lady.

In an open letter in Newsweek magazine, Stephanopoulos advises her to “face it head on and dispel it quickly.”